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Glass transition and state diagram for fresh and freeze-driedChinese gooseberry

Haiying Wang, Shaozhi Zhang, Guangming Chen *

Institute of Refrigeration and Cryogenics, Zhejiang University, Hangzhou 310027, China

Received 15 October 2006; received in revised form 12 May 2007; accepted 14 May 2007Available online 26 May 2007

Abstract

The glass transition temperature and freezing temperature of Chinese gooseberry, which is also called kiwi fruit, prepared at variouswater activities at 25 C were determined by differential scanning calorimetry (DSC), and used to plot the state diagram for the Chinesegooseberry sample. High moisture content (>0.45, dry basis) samples obtained by adding liquid water into freeze-dried samples, werealso analyzed. The state diagram was composed by the freezing curve and the glass transition line, which were fitted according to Clau-siusClapeyron model and GordonTaylor model, respectively. The maximal-freeze-concentration point was calculated to be at a mois-ture content ofX0s 0:153 (g water/g wet basis) and at this point T

0m 41:8

C, T0g 57:1C. The state diagram could be used to

predict the stability during storage and the necessary storing conditions for Chinese gooseberry products. 2007 Elsevier Ltd. All rights reserved.

Keywords: State diagram; Glass transition; Freeze-dried; Chinese gooseberry

1. Introduction

One of the explanations for the behavior of food mate-rials during processing and storage is based on the foodpolymer theory (Rahman, 1995). According to this theory,before freezing completely, most products experience glasstransition. The glass transition phenomenon happens notat one temperature point but in a temperature range duringwhich the products become non-crystalline solids from arubbery or leathery state and the products stabilityincrease greatly. When the storage temperature is above

the glass transition temperature, some molecules will bemobile, leading to undesirable reactions.State diagram assists in predicting food stability during

storage as well as selecting a suitable condition of temper-ature and moisture content for processing (Rahman, 1995;Roos, 1995). A state diagram usually shows freezing curveand glass transition line, and maximal-freeze-concentration

point can be found on it. Differential scanning calorimetry(DSC) is often used in state diagram research.

Since real foods are complex multi-component mix-tures which have variable compositions even for the samebreed, very little data about their state diagrams havebeen accumulated compared with pure solutions. How-ever, as the importance of state diagram is better recog-nized, more studies have been carried out for real foodsduring recent years. State diagrams of processed apple(Aguilera, Cuadros, & del Valle, 1998; Bai, Rahman, Per-era, Smith, & Melton, 2001; Sa, Figueiredo, & Sereno,

1999), pineapple (Telis & Sobral, 2001), tomato (Baroni,Sereno, & Hubinger, 2003; Telis & Sobral, 2002), corn-starch (Zhong & Sun, 2005), tuna meat (Rahman, Kasa-pis, Guizani, & Al-Amri, 2003) and garlic (Rahman,Sablani, Al-Habsi, Al-Maskri, & Al-Belushi, 2005) havebeen reported.

Chinese gooseberry (scientific identification: ActinidiaChinensis, which is also called kiwi fruit) is rich in vitaminC, carbohydrate, fibre, folic acid, pantothenic acid, cal-cium, protein, magnesium, iron, vitamin B6 and carotene.It is even described as king of the fruits for its high nutritive

0260-8774/$ - see front matter 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jfoodeng.2007.05.024

* Corresponding author. Tel./fax: +86 571 8795 1680.E-mail address: [email protected] (G. Chen).

www.elsevier.com/locate/jfoodeng

Journal of Food Engineering 84 (2008) 307312
mailto:[email protected]:[email protected]


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value. Since the production of Chinese gooseberry isrestricted by area and season, long term preservation isattractive (Gerschenson, Rojas, & Marangoni, 2001; Lee,Farid, & Nguang, 2006). The objective of this study is todevelop a state diagram for Chinese gooseberry by DSCtechnique.

2. Materials and methods

Fresh Chinese gooseberry was bought from local mar-ket. Its moisture content was determined by placing smallsample pieces in a drying oven (DHG-9070, Jinghong,China) at 60 C for 3 h and then at 100 C for 5 h(Han, 1996). The weights of the samples were recordedeach hour until they showed variation less than 0.3%(Sa et al., 1999). The results were given as an averagefor three samples.

In order to prepare samples with different water content,fresh Chinese gooseberry were cut into cylinders, with3 mm in height and 4 mm in diameter. Such cylinders werethen put into a freeze-dryer (Self-made, Weng, Zhou,Chen, Wang, & Xia, 2004). The samples were completelyfrozen at 60 C, followed by drying at about 10 Pa,20 C for 20 h and then 20 C for 5 h. All the sampleswere powdered and further dried in a desiccator overP2O5 for 13 weeks for completely dried materials (Roos& Karel, 1991). To get samples with water activity from0.12 to 0.94, powdered freeze-dried Chinese gooseberrysamples were put in DSC pans (45 mg) and equilibratedwith saturated salt solutions of constant water activities(Table 1) for 2448 h (Roos & Karel, 1991) and moisturecontent (dry basis) values were obtained from the weight

differences of the samples before and after equilibration.

To get samples with water activity higher than 0.94, waterwas added directly by micro-syringe into the freeze-driedpowder in small aluminum DSC pans and then the panswere sealed and put in a dry desiccator at 4 C for 24 h(Telis & Sobral, 2001). The weight gains after equilibrationwere measured and used to calculate the water contents of

the samples.The relationship between water activity and moisture

content (dry basis) is correlated with the GuggenheimAndersonde Boer (GAB) model (Eqn. (1)).

Xw XmCKaw

1 Kaw1 Kaw CKaw1

where Xw is the moisture content in dry basis; Xm is themoisture content at fully occupied active sorption sites withone molecule of water, which is secure moisture content forhigh quality preservation of freeze-dried food; Cand Karethe GAB parameters associated with the enthalpies of

monolayer and multilayer, respectively.

Table 1Water activity of saturated salt solutions at 25 C (Sa et al., 1999; Roos,1987)

Saturated salt solution a25w

LiCl 0.12CH3COOK 0.23MgCl2 6H2O 0.33K2CO3 0.44

Mg(NO3)2 6H2O 0.52NaNO2 0.61NaCl 0.75KCl 0.85KNO3 0.94

Nomenclature

aw water activityC GAB parameterC1, C2 general constants in WLF equation

K GAB parameterK GordonTaylor parameterE molecular mass ration of water to solids (kw/ks)DHm melting enthalpy (J/g)R2 significance of correlation coefficientT0g maximally freeze-concentration glass transition

temperature (C)T00g characteristic temperature of intersection of

glass transition and freezing lines (C)T000g characteristic glass transition temperature mea-

sured by DSC (C)Tgm glass transition temperature of mixture (C)Tgs glass transition temperature of solids (C)

Tgw glass transition temperature of water (C)TF freezing temperature (C)T0m end point of freezing (C)

T0m maximally freeze-concentration freezing temper-ature (C)

Tw freezing point of water (C)

Xm moisture content at fully occupied active sorp-tion sites with one molecule of water (g/g drybasis)

X0s solid content at the maximally freeze-concentra-tion (g solids/g wet basis)

X00s solids mass fraction at T00g (kg solids/kg sample)

X000s solids mass fraction at Tg000 (kg solids/kg sample)

X0s initial mass fraction of solids in equation (g sol-ids/g wet basis)

Xs mass fraction of solids (g solids/g wet basis)Xw mass fraction of water (g water/g basis)b molar freezing point constant of water

(1860 kg K/kg mol)

kw molecular mass of waters time constants for crystallization at Tgisg time constants for crystallization at T

308 H. Wang et al. / Journal of Food Engineering 84 (2008) 307312


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The transition temperatures of Chinese gooseberry sam-ples at different moisture contents were measured with dif-ferential scanning calorimetry (DSC-Q100, TA, USA). Theinstrument was calibrated for heat flow and temperatureusing distilled water (melting point 0.0 C, DHm = 333 J/g) and indium (melting point 156.6 C, DHm = 28.44 J/g)

(Chinese Standard GB/T 13464-92). An empty aluminumpan was used as reference. Samples were sealed in alumi-num pans (1.75 mm height; 6.67 mm internal diameter)and nitrogen was used as carrier gas (50 mL/min). Liquidnitrogen was used for sample cooling with a cooling rateof 10 C/min. All the scans were taken at the same heatingrate (10 C/min) between 120 and 25 C. Annealing wasperformed holding the samples at the temperature pointT0m3.0 C for 30 min (Bai et al., 2001). All the results weregiven as an average for three samples.

The glass transition temperature of foods with low wateractivities is modeled by GordonTaylor equation (Eqn. (2))(Bai et al., 2001; Sa et al., 1999; Telis & Sobral, 2001).

Tgm XsTgs kXwTgw

Xs kXw2

where Xs and Xw are the mass fraction of solids and water(wet basis), respectively; Tgm, Tgs and Tgw are the glasstransition temperature of mixture, solids and water, respec-tively. Tgw = 135.0 C (Sa et al., 1999); k is the GordonTaylor parameter.

3. Result and discussion

The moisture content measured for fresh Chinese goose-

berry was (0.84 0.01) (g water/g wet basis), which wasclose to the reference data 0.8341 or 0.8382 (g water/g wetbasis).

The sorption experimental data were fitted with theGAB model. Sorption isotherm is shown in Fig. 1. Onthe whole, the GAB model well fits the experimental data.The empirical parameters and correlation coefficients cal-culated by non-linear regression are listed in Table 2. SinceChinese gooseberry is also a fruit with large content offructose and small content of polymer, its sorption iso-therm presents a shape of J, similar with those obtainedby Telis (Telis & Sobral, 2001).

Freezing points and glass transitions of samples at dif-

ferent moisture contents were determined from heat flowcurves with professional software (Universal Analysis,TA, USA), as shown in Figs. 2 and 3. Here, the onset tem-perature (Tgi) of the glass transition region is defined as theintersection of the first and the second tangent and consid-ered as the glass transition temperature. The mid-point(Tgp) is defined as the inflexion of the curve part betweenthe first and the third tangent. The end point (Tgp) isdefined as the intersection of the second and third tangent.

The freezing point (TF) is taken as the temperature at endo-thermic peak (Fig. 2). The end point of freezing (T0m) istaken as the initial point of ice melting at endothermicpeak. (Rahman, 2006; Rahman et al., 2005).

The samples with different water content behaved differ-ently during DSC tests. For samples with moisture contentless than 0.19 (g water/g wet basis), since much of the water

were linked to the solid matrix, only the phenomenon of

1 Ref.: http://www.mcgill.ca/cine/resources/data/miao/.2 Ref.: http://www.food-allergens.de/symposium-vol1(1)/data/kiwi/

kiwi-composition.htm.

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Equlibriumm

oisturecontent

(gwater/g

drybasis)

Water activity

Fig. 1. Sorption isotherm of Chinese gooseberry (j experimental data; GAB model).

Table 2Model fitting for sorption experimental data

Models Freeze-dried apple(Sa et al., 1999)

Freeze-driedpineapple (Telis &Sobral, 2001)

Freeze-driedChinese gooseberry

GAB model

Xm 0.112a 0.112b 7.190a 7.916b 0.459

C 2.093a 1.955b 0.012a 0.010b 0.265K 0.985a 0.987b 0.815a 0.821b 0.827R2GAB 0.994

a 0.997b 0.991a 0.985b 0.987

a Parameters from the references (Sa et al., 1999; Telis & Sobral, 2001).b Parameters modeled with the data from the references (Sa et al., 1999;

Telis & Sobral, 2001).

Fig. 2. Freezing point determination on DSC thermogram (Moisturecontent 0.504 (g water/g wet basis)).

H. Wang et al. / Journal of Food Engineering 84 (2008) 307312 309
http://www.mcgill.ca/cine/resources/data/miao/http://www.food-allergens.de/symposium-vol1(1)/data/kiwi/kiwi-composition.htmhttp://www.food-allergens.de/symposium-vol1(1)/data/kiwi/kiwi-composition.htmhttp://www.food-allergens.de/symposium-vol1(1)/data/kiwi/kiwi-composition.htmhttp://www.food-allergens.de/symposium-vol1(1)/data/kiwi/kiwi-composition.htmhttp://www.mcgill.ca/cine/resources/data/miao/


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glass transition could be observed. Tgi decreased from23.2 C to 60.8 C when the moisture content increasedfrom 0.0 to 0.19 (g water/g wet basis) (Table 3).

When the moisture content was in the range from 0.32to 0.40 (g water/g wet basis), an exothermic recrystallisa-tion (devitrification) peak of unfrozen water was observedas shown in Fig. 4. The devitrification could be eliminatedby annealing the sample (Fig. 5). The freezing temperatureat the maximal-freeze-concentration point, T0m, was41.8C (Table 4). When the moisture content was higherthan 0.50 (g water/g wet basis), the glass transition phe-nomenon disappeared and only the melting peak couldbe found (Table 4).

With the DSC data, the state diagram of Chinese goose-

berry flesh could be drawn as shown in Fig. 6. The glasstransition data were fitted with GordonTaylor equationusing non-linear regression method and the values of Tgs,Tgw and k are listed in Table 5.

ClausiusClapeyron equation (Eqn. (3)) well representsthe decreased freezing temperature with the increasing solid

Fig. 3. Glass transition determination on DSC thermogram (Moisturecontent 0.175 (g water/g wet basis)).

Table 3

Glass transition temperature of Chinese gooseberry when there is noformation of ice

Solid content Xs (g solid/g wet basis) Tgi/C Tgm/C Tge/C

0.81 60.8 55.8 52.20.83 56.6 53.4 49.10.85 60.6 55.8 52.70.87 45.2 40.9 37.30.93 25.5 18.7 14.30.95 24.4 19.8 13.71.00 23.2 35.8 45.7

Fig. 4. DSC thermogram for non-annealed sample (Moisture content

0.338 (g water/g dry basis)).

Fig. 5. DSC thermogram for annealed sample (Moisture content 0.333 (gwater/g wet basis)).

Table 4Glass transition temperature and freezing point of Chinese gooseberrywhen there is freezable water

SolidcontentXs (g solid/g wet basis)

Tgi T000g =

C Tgm/C Tge/C T0m=

C TF/C DHsample/kJ/kg

0.20 29.6 2.2 172.20.30 33.2 2.7 170.60.53 61.1 55.2 51.6 39.6 7.7 102.40.65 59.8 54.9 52.0 33.6 19.0 34.50.67 48.1 41.6 39.1 41.3 21.1 33.30.69 60.5 55.0 51.3 41.8 19.7 40.1

0.0 0.2 0.4 0.6 0.8 1.0-140

-120

-100

-80

-60

-40

-20

0

20

40

X//'

s=0.835

T///

g=-60.8

oC

X//

s=0.871

T//

g=-49.2

oC

Temperature(oC

)

Solids (fraction)

T/

m=-41.8

X/

s=0.847

T/

g=-57.1

oC

A

G

B/

F

D

E

C

Fig. 6. State diagram of Chinese gooseberry sample (AB0: freezing curve;DE: glass transition line; F: glass transition point of maximally freeze-

concentration).



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content in the range from 0.2 to 0.7 (g solids/g wet basis)with R2 = 0.928.

D b

kwln

1 X0s1 X0s EX

0s

3

where D is the freezing point depression (Tw TF); TF isthe freezing point of the sample (C); Tw is the freezingpoint of water (C); b is the molar freezing point constantof water (1860 kg K /kg mol); kw is the molecular mass ofwater; X0s is the initial solids mass fraction (kg solids/kg sample); and E is the molecular mass ration of waterto solids (kw/ks), E= 0.101.

In Fig. 6, line AB0 represents freezing temperature curveand line DE represents glass transition temperature Tgi.Several characteristic points B0, G, F and C are clearlydefined by (Rahman et al., 2005). Point B0 is the maxi-mal-freeze-concentration point, at which the freezing tem-

perature T0m 41:8

C and the water content(1 X0s 0:153 (g water/g wet basis). This part of wateris considered as unfreezable (Rahman et al., 2005). PointF is the maximal-freeze-concentration glass transitionpoint, its temperature T0g 57:2

C and its solid contentis the same as X0s at point B

0; point G (T00g 49:2C and

X00s 0:871 (g water/g wet basis)) is the intersection of lineAB0 and line DE, which is different from the experimentalvalue (Tgi = 45.2 C and Xs = 0.871 (g water/g wetbasis)) in Table 3. This difference is due to the discrepancyof the fitted curves from the experimental data. Point Crepresents the glass transition of high water content sam-ples measured by DSC with annealing, its temperature(T000g=60.8 C and X

000s =0.835 (g water/g wet basis)).

There are numbers of factors which can influence foodstability (Rahman, 2006). Among them temperature isprominent. Low temperature cannot only slow down theadverse reactions of microbe, enzyme, respiration andother factors, but also suppress the growth of ice crystals.Big ice crystals may destroy the micro-structures of foodproduct and lead to the decline of food quality. Withunderstanding of the state diagram, the best storing condi-tion for products could be proposed. For example, for Chi-nese gooseberry dried to water content of 0.1 (g water/g wet basis), it had better be stored below its glass transi-

tion point, 38.3 C. For products that have to be stored

above the glass transition temperature, WilliamsLandelFerry (WLF) equation (Roos, 1995) could be employedto estimate their shelf life. WLF equation is given asfollows:

logs

sg

C1T Tg

C2 T Tg4

where sg and s are time constants for crystallization at Tgand T, respectively; C1 and C2are general constants.According to Sun (Sun, 1997), for the system which has afreezing point much higher than its glass transition point,C1 = 20 and C2 = 155. The storage period under glassstate, sg, is estimated as follows: since the growth rate ofice crystal under glass state is estimated as 1 mm per 103

years (Hua, Li, & Liu, 1999), it will take 2030 years fora trivial crystal to grow big enough to destroy the Chinesegooseberry cells whose typical diameters are about 2030 lm, therefore sg equals 2030 years. As an example, letsconsider dried Chinese gooseberry product with water con-

tent Xw = 0.1 (g water/g wet basis), its glass transition tem-perature can be found from the diagram to be 38.3 C.According to (Eq. (4)), the shelf life of this product at5 C can then be calculated to be 3.2 and 5.0 days. It iseasy to make similar estimation for products with otherwater contents and stored at other temperatures.

4. Conclusions

Chinese gooseberry is one of the most popular andnutritive fruits that is worthy for storage. The state dia-gram of freeze-dried Chinese gooseberry was drawn

according to DSC data in this paper. It is composed offreezing line and glass transition line. The glass transitiontemperature for the maximal-freeze-concentrated condi-tion, T0g, was found to be 57.2 C. T

0m, the freezing tem-

perature for the maximal-freeze-concentrated conditionwas found to be 41.8 C. The unfreezable water fractionwas found to be 0.153 (g water/g wet basis). The state dia-gram obtained here may be helpful in developing betterproducts made of Chinese gooseberry.

Acknowledgements

The authors acknowledge the financial supports fromNational Natural Science Foundation of China (No.50076039) and National Foundation for Scholars Return-ing from Abroad.

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Table 5GordonTaylor model fitting for experimental data

Parameters Heat pump driedapple (Bai et al.,2001)

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Freeze-driedChinesegooseberry

GordonTaylor model

Tgs (C) 41.3 57.75 23.2

Tgw (C) 134.8 135.15 135k 3.59 0.21 5.72R2 0.954 0.972

Results

T0g C 57.8 51.6 57.2

T0m C 50.3 52.0 41.8

H. Wang et al. / Journal of Food Engineering 84 (2008) 307312 311


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